How to Solve Cake and Pipe Equations: Helpful Tips and Solutions

  • Thread starter Adam Rabe
  • Start date
In summary, the conversation discusses two problems involving pipes and a cake. The correct answers for the pipe problem should be A) and for the cake problem should be E). The solution for the pipe problem involves finding the scaling of the radius, while the solution for the cake problem involves scaling all dimensions by the same factor.
  • #1
Adam Rabe
33
0

Homework Statement


pipe factor question.PNG
cake volume.PNG


Homework Equations


Cake one...
Area of circle times height
Pipe one... Av = Av

The Attempt at a Solution


Hello, i would like some help in the right direction/
I had a go at these problems and got B) for the pipe one and C for the cake one.
However the correct answers for the pipe one is A) whereas the one for the cake is E.).

I don't understand what I am doing wrong. If you try substituting values and work backwards the constants i get don't fit.
EG: for the pipe one i made r = 4...
pi * 4^2 * 0.5 = pi* x * 4^2 * 2
x = 0.25 so i got B, but the correct answer is A...

For the cake problem i made h=5 and diametre = 8cm (radius = 4)...
pi * 4^2 * 5 = 251 m-3
i then doubled volume, and worked backwards to find factor to increase radius and therefore diamtre by...

502 = pi * r^2 * 5
r = 5.6418
5.6418/4 = 1.44... so i got C, but correct answer is E

Please help me
 
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  • #2
Pipe: if x is the scaling of the radius, you should have pi*x^2*4^2*2
Cake: it is a scale model, so all dimensions increase by the same factor: pi*x^2*4^2*x*5 = 502
 
  • #3
mjc123 said:
Pipe: if x is the scaling of the radius, you should have pi*x^2*4^2*2
Cake: it is a scale model, so all dimensions increase by the same factor: pi*x^2*4^2*x*5 = 502
Hello, thank you so much! I get the one with the pipe, but i don't quite get the second one, where did the other x come from? Do you have a site i can read up on to explain this I'm too stupid.
 
  • #4
Adam Rabe said:
Hello, thank you so much! I get the one with the pipe, but i don't quite get the second one, where did the other x come from? Do you have a site i can read up on to explain this I'm too stupid.
It says it is a scale model, so all dimensions increase in the same ratio. If the cake starts with radius r and height h, and all dimensions are scaled up by a factor x, what is the new radius? What is the new height? What is the new volume?
 

FAQ: How to Solve Cake and Pipe Equations: Helpful Tips and Solutions

How do I know which equation to use for a specific cake or pipe problem?

When solving cake and pipe equations, it is important to carefully read and understand the problem. Look for keywords such as "filling," "emptying," "rate," and "time" to determine which equation to use. Additionally, drawing a diagram and labeling the values given in the problem can also help identify the correct equation to use.

What are some common mistakes to avoid when solving cake and pipe equations?

One common mistake is forgetting to convert units to the same measurement system. Make sure all values are in the same units before plugging them into the equation. Another common mistake is mixing up the variables in the equation. Always double check which variable represents what in the equation before solving.

How can I check my answer to make sure it is correct?

After solving the equation, plug the values back into the original problem to see if they make sense. For cake problems, the final volume of the cake should match the initial volume plus any added or removed volume. For pipe problems, the rate of filling/emptying should match the given rate and time period.

Are there any shortcuts or tricks for solving cake and pipe equations?

One helpful trick is to remember that the rate of filling/emptying is equal to the volume divided by the time. This can help simplify the equations and make them easier to solve. Additionally, practicing with different types of problems can help improve problem-solving skills for cake and pipe equations.

Can I use the same equations for both cake and pipe problems?

Yes, the same equations can be used for both cake and pipe problems. The only difference is how the variables are interpreted and labeled. For cake problems, the variables represent the volume of the cake, while for pipe problems, the variables represent the rate of filling/emptying.

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